Question

The data set below has 7 values.

Find the mean absolute deviation for the data set.
If necessary, round your answer to the nearest hundredth.
15, 5, 12, 14, 18, 16, 4
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Mean absolute deviation:
X

Answer 1

4.29 (nearest hundredth)

Explanation:

Given data set:

• 15, 5, 12, 14, 18, 16, 4

To find the mean absolute deviation:

Step 1

Calculate the mean:

`\textsf{Mean}=(15+5+12+14+18+16+4)/(7)=12`

Step 2

Calculate the absolute deviations - how far away each data point is from the mean using positive distances.

`\begin{array}c\vphantom{\frac12} \sf Data \; point & \sf Distance \; from \; mean\\\cline{1-2} \vphantom{\frac12} 15 & |15-12|=3\\\vphantom{\frac12} 5 & |5-12|=7\\\vphantom{\frac12} 12 & |12-12|=0\\\vphantom{\frac12} 14 & |14-12|=2\\\vphantom{\frac12} 18 & |18-12|=6\\\vphantom{\frac12} 16 & |16-12|=4\\\vphantom{\frac12} 4 & |4-12|=8\end{array}`

Step 3

Add the absolute deviations together:

`\implies 3+7+0+2+6+4+8=30`

Step 4

Divide the sum of the absolute deviations by the number of data points:

`\implies (30)/(7)=4.29`